\(\text{Ta có:}\)
\(\text{Để}\)\(\frac{4b+42}{b+7}\)\(\text{nguyên thì}\)\(4b+42⋮b+7\)
\(\text{Lại có:}\)
\(\text{4b + 42 = 4b + 28 + 14 = 4( b+7 ) + 14}\)
\(\text{Vì}\)\(b+7⋮b+7\)\(\Rightarrow4\left(b+7\right)⋮b+7\)
\(\text{Do đó:}\)\(14⋮b+7\)
\(\Rightarrow b+7\inƯ\left(14\right)=\left\{1;2;7;14\right\}\)
\(\Rightarrow b\in\left\{-6;-5;0;7\right\}\)